The full-back is available on a free transfer with his Liverpool contract due to run out at the end of the season - and Madrid are on the verge of competing a deal to sign him, report Relevo. Other than that addition, the club plan to save other big decisions until May, but there is little expectation that much will be done.
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THE BIGGER PICTURE
The reigning La Liga champions are said to be very happy with the squad in its current state. Right-back is a major priority, hence the Alexander-Arnold interest, but every other option is stocked with experience and exciting young players. Left-back may be looked at but there is no firm target in mind.
DID YOU KNOW?
There are two scenarios in which Madrid may look to do more business than currently intended. One is if they fail to win either of the major trophies they are currently fighting for - La Liga and the Champions League. The other is if an unexpected departure is sanctioned, with Vinicius Junior linked with a move to the Saudi Pro League.
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WHAT NEXT FOR REAL MADRID?
The club are calm and confident of defending their La Liga and Champions League double this season. After facing Real Sociedad in the Copa del Rey on Wednesday, they will play Real Betis in the league on Saturday before beginning their Champions League last-16 tie with city rivals Atletico Madrid next week.